Question: In a recent basketball game, Shenille attempted only three-point shots and two-point shots.  She was successful on $20\%$ of her three-point shots and $30\%$ of her two-point shots.  Shenille attempted $30$ shots.  How many points did she score?
Let the number of attempted three-point shots made be $x$ and the number of attempted two-point shots be $y$.  We know that $x+y=30$.   We need to evaluate $(0.2\cdot3)x +(0.3\cdot2)y$, as we know that the three-point shots are worth 3 points and that she made $20\%$ of them and that the two-point shots are worth 2 and that she made $30\%$ of them.

Simplifying, we see that this is equal to $0.6x + 0.6y = 0.6(x+y)$.  Plugging in $x+y=30$, we get $0.6(30) = \boxed{18}$.